Runs one step of the RWM algorithm with symmetric proposal.

Random Walk Metropolis is a gradient-free Markov chain Monte Carlo (MCMC) algorithm. The algorithm involves a proposal generating step proposal_state = current_state + perturb by a random perturbation, followed by Metropolis-Hastings accept/reject step. For more details see Section 2.1 of Roberts and Rosenthal (2004).

mcmc_random_walk_metropolis(
  target_log_prob_fn,
  new_state_fn = NULL,
  seed = NULL,
  name = NULL
)

Arguments

target_log_prob_fn	Function which takes an argument like current_state ((if it's a list current_state will be unpacked) and returns its (possibly unnormalized) log-density under the target distribution.
new_state_fn	Function which takes a list of state parts and a seed; returns a same-type list of Tensors, each being a perturbation of the input state parts. The perturbation distribution is assumed to be a symmetric distribution centered at the input state part. Default value: NULL which is mapped to tfp$mcmc$random_walk_normal_fn().
seed	integer to seed the random number generator.
name	String name prefixed to Ops created by this function. Default value: NULL (i.e., 'rwm_kernel').

Value

a Monte Carlo sampling kernel

Details

The current class implements RWM for normal and uniform proposals. Alternatively, the user can supply any custom proposal generating function. The function one_step can update multiple chains in parallel. It assumes that all leftmost dimensions of current_state index independent chain states (and are therefore updated independently). The output of target_log_prob_fn(current_state) should sum log-probabilities across all event dimensions. Slices along the rightmost dimensions may have different target distributions; for example, current_state[0, :] could have a different target distribution from current_state[1, :]. These semantics are governed by target_log_prob_fn(current_state). (The number of independent chains is tf$size(target_log_prob_fn(current_state)).)

See also

Other mcmc_kernels: mcmc_dual_averaging_step_size_adaptation(), mcmc_hamiltonian_monte_carlo(), mcmc_metropolis_adjusted_langevin_algorithm(), mcmc_metropolis_hastings(), mcmc_no_u_turn_sampler(), mcmc_replica_exchange_mc(), mcmc_simple_step_size_adaptation(), mcmc_slice_sampler(), mcmc_transformed_transition_kernel(), mcmc_uncalibrated_hamiltonian_monte_carlo(), mcmc_uncalibrated_langevin(), mcmc_uncalibrated_random_walk()